The sudden death of entanglement is investigated for the non-Markovian dynamic process of a pair of interacting flux qubits under a thermal bath. The results show that, for initially two-qubit entangled states, entang...The sudden death of entanglement is investigated for the non-Markovian dynamic process of a pair of interacting flux qubits under a thermal bath. The results show that, for initially two-qubit entangled states, entanglement sudden death （ESD） always happens in the thermal reservoir, where its appearance strongly depends on the environment. In particular, ESD of the qubits occurs more easily for the non-Markovian process than for the Markovian one.展开更多
The exact dynamics of an open quantum system consisting of one qubit driven by a classical driving field is investigated. Our attention is focused on the influences of single-and two-photon excitations on the dynamics...The exact dynamics of an open quantum system consisting of one qubit driven by a classical driving field is investigated. Our attention is focused on the influences of single-and two-photon excitations on the dynamics of quantum coherence and quantum entanglement. It is shown that the atomic coherence can be improved or even maintained by the classical driving field, the non-Markovian effect, and the atom-reservoir detuning. The interconversion between the atomic coherence and the atom-reservoir entanglement exists and can be controlled by the appropriate conditions. The conservation of coherence for different partitions is explored, and the dynamics of a system with two-photon excitations is different from the case of single-photon excitation.展开更多
An explicit form of reliability and economical stationary performance indexes for monotonous multicomponent system with regard to its elements’ maintenance has been found. The maintenance strategy investigated suppos...An explicit form of reliability and economical stationary performance indexes for monotonous multicomponent system with regard to its elements’ maintenance has been found. The maintenance strategy investigated supposes preventive maintenance execution for elements that has attained certain operating time to failure. Herewith for the time period of elements’ maintenance or restoration operable elements, functionally connected with the failed ones, are deactivated. The problems of maintenance execution frequency optimization have been solved. For the model building the theory of semi-Markovian processes with a common phase field of states is used.展开更多
A risk model with Markovian arrivals and tax payments is considered.When the insurer is in a profitable situation,the insurer may pay a certain proportion of the premium income as tax payments.First,the Laplace transf...A risk model with Markovian arrivals and tax payments is considered.When the insurer is in a profitable situation,the insurer may pay a certain proportion of the premium income as tax payments.First,the Laplace transform of the time to cross a certain level before ruin is discussed.Second,explicit formulas for a generalized Gerber-Shiu function are established in terms of the＇original＇Gerber-Shiu function without tax and the Laplace transform of the first passage time before ruin.Finally,the differential equations satisfied by the expected accumulated discounted tax payments until ruin are derived.An explicit expression for the discounted tax payments is also given.展开更多
An explicit form of reliability and economical stationary performance indexes for monotonous multicomponent system with regard to its elements’ maintenance has been found. The maintenance strategy investigated suppos...An explicit form of reliability and economical stationary performance indexes for monotonous multicomponent system with regard to its elements’ maintenance has been found. The maintenance strategy investigated supposes preventive maintenance execution for elements that has attained certain operating time to failure. Herewith for the time period of elements’ maintenance or restoration operable elements are not deactivated. The problems of maintenance execution frequency optimization have been solved. For the model building the theory of semi-Markovian processes with a common phase field of states is used.展开更多
Mathematical model of control of restorable system with latent failures has been built. Failures are assumed to be detected after control execution only. Stationary characteristics of system operation reliability and ...Mathematical model of control of restorable system with latent failures has been built. Failures are assumed to be detected after control execution only. Stationary characteristics of system operation reliability and efficiency have been defined. The problem of control execution periodicity optimization has been solved. The model of control has been built by means of apparatus of semi-Markovian processes with a discrete-contin- uous field of states.展开更多
Semi-Markovian model of control of restorable system with latent failures has been built with regard to control errors. Stationary reliability and efficiency characteristics of its operation have been found. The probl...Semi-Markovian model of control of restorable system with latent failures has been built with regard to control errors. Stationary reliability and efficiency characteristics of its operation have been found. The problem of control execution periodicity optimization has been solved.展开更多
The aim of this work is mathematical education through the knowledge system and mathematical modeling. A net model of formation of mathematical knowledge as a deductive theory is suggested here. Within this model the ...The aim of this work is mathematical education through the knowledge system and mathematical modeling. A net model of formation of mathematical knowledge as a deductive theory is suggested here. Within this model the formation of deductive theory is represented as the development of a certain informational space, the elements of which are structured in the form of the orientated semantic net. This net is properly metrized and characterized by a certain system of coverings. It allows injecting net optimization parameters, regulating qualitative aspects of knowledge system under consideration. To regulate the creative processes of the formation and realization of mathematical know- edge, stochastic model of formation deductive theory is suggested here in the form of branching Markovian process, which is realized in the corresponding informational space as a semantic net. According to this stochastic model we can get correct foundation of criterion of optimization creative processes that leads to “great main points” strategy (GMP-strategy) in the process of realization of the effective control in the research work in the sphere of mathematics and its applications.展开更多
In this paper, we discuss a discrete time repairable queuing system with Markovian arrival process, where lifetime of server, service time and repair time of server are all discrete phase type random variables. Using...In this paper, we discuss a discrete time repairable queuing system with Markovian arrival process, where lifetime of server, service time and repair time of server are all discrete phase type random variables. Using the theory of matrix geometric solution, we give the steady state distribution of queue length and waiting time. In addition, the stable availability of the system is also provided.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No.10864002)
文摘The sudden death of entanglement is investigated for the non-Markovian dynamic process of a pair of interacting flux qubits under a thermal bath. The results show that, for initially two-qubit entangled states, entanglement sudden death （ESD） always happens in the thermal reservoir, where its appearance strongly depends on the environment. In particular, ESD of the qubits occurs more easily for the non-Markovian process than for the Markovian one.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61675115,11204156,11574178,11304179,and 11647172)the Science and Technology Plan Projects of Shandong University,China(Grant No.J16LJ52)
文摘The exact dynamics of an open quantum system consisting of one qubit driven by a classical driving field is investigated. Our attention is focused on the influences of single-and two-photon excitations on the dynamics of quantum coherence and quantum entanglement. It is shown that the atomic coherence can be improved or even maintained by the classical driving field, the non-Markovian effect, and the atom-reservoir detuning. The interconversion between the atomic coherence and the atom-reservoir entanglement exists and can be controlled by the appropriate conditions. The conservation of coherence for different partitions is explored, and the dynamics of a system with two-photon excitations is different from the case of single-photon excitation.
文摘An explicit form of reliability and economical stationary performance indexes for monotonous multicomponent system with regard to its elements’ maintenance has been found. The maintenance strategy investigated supposes preventive maintenance execution for elements that has attained certain operating time to failure. Herewith for the time period of elements’ maintenance or restoration operable elements, functionally connected with the failed ones, are deactivated. The problems of maintenance execution frequency optimization have been solved. For the model building the theory of semi-Markovian processes with a common phase field of states is used.
基金Supported by the National Natural Science Foundation of China(10971230,11171179)the Natural Science Foundation of Shandong Province(ZR2010AQ015)the Tianyuan Fund for Mathematics(11126232)
文摘A risk model with Markovian arrivals and tax payments is considered.When the insurer is in a profitable situation,the insurer may pay a certain proportion of the premium income as tax payments.First,the Laplace transform of the time to cross a certain level before ruin is discussed.Second,explicit formulas for a generalized Gerber-Shiu function are established in terms of the＇original＇Gerber-Shiu function without tax and the Laplace transform of the first passage time before ruin.Finally,the differential equations satisfied by the expected accumulated discounted tax payments until ruin are derived.An explicit expression for the discounted tax payments is also given.
文摘An explicit form of reliability and economical stationary performance indexes for monotonous multicomponent system with regard to its elements’ maintenance has been found. The maintenance strategy investigated supposes preventive maintenance execution for elements that has attained certain operating time to failure. Herewith for the time period of elements’ maintenance or restoration operable elements are not deactivated. The problems of maintenance execution frequency optimization have been solved. For the model building the theory of semi-Markovian processes with a common phase field of states is used.
文摘Mathematical model of control of restorable system with latent failures has been built. Failures are assumed to be detected after control execution only. Stationary characteristics of system operation reliability and efficiency have been defined. The problem of control execution periodicity optimization has been solved. The model of control has been built by means of apparatus of semi-Markovian processes with a discrete-contin- uous field of states.
文摘Semi-Markovian model of control of restorable system with latent failures has been built with regard to control errors. Stationary reliability and efficiency characteristics of its operation have been found. The problem of control execution periodicity optimization has been solved.
文摘The aim of this work is mathematical education through the knowledge system and mathematical modeling. A net model of formation of mathematical knowledge as a deductive theory is suggested here. Within this model the formation of deductive theory is represented as the development of a certain informational space, the elements of which are structured in the form of the orientated semantic net. This net is properly metrized and characterized by a certain system of coverings. It allows injecting net optimization parameters, regulating qualitative aspects of knowledge system under consideration. To regulate the creative processes of the formation and realization of mathematical know- edge, stochastic model of formation deductive theory is suggested here in the form of branching Markovian process, which is realized in the corresponding informational space as a semantic net. According to this stochastic model we can get correct foundation of criterion of optimization creative processes that leads to “great main points” strategy (GMP-strategy) in the process of realization of the effective control in the research work in the sphere of mathematics and its applications.
文摘In this paper, we discuss a discrete time repairable queuing system with Markovian arrival process, where lifetime of server, service time and repair time of server are all discrete phase type random variables. Using the theory of matrix geometric solution, we give the steady state distribution of queue length and waiting time. In addition, the stable availability of the system is also provided.
